A random sample of 600 adults is taken from a population of over one million, in order to compute a con dence interval for a proportion. If the researchers wanted to decrease the width of the con dence interval, they could A. increase the size of the sample. B. decrease the size of the population. C. increase the size of the population. D. decrease the size of the sample.

Option A: Increase the size of the sample.

Given that:

Population size = 1 million

Sample size = 600

Confidence interval(CI) is an interval as the name suggests which has values that are likely to occur with a certain confidence level.

The formula for calculating CI is:

where the symbols mean:

CI = confidence interval

: sample mean

z = confidence level

s = sample standard deviation

n = size of sample.

To decrease the width, of given CI, we will need to decrease the magnitude of   .

For that, as we increase n, the magnitude will automatically go down.

Since n denotes the size of sample, thus we need to increase the size of sample to decrease the confidence interval's width.

Thus option A: increase the size of the sample is correct.

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A. increase the size of the sample.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The width of the interval is given by:

So as n(the size of the sample) increases, the width decreases.

If the researchers wanted to decrease the width of the con dence interval, they could

The correct answer is:

Increase n, that is

A. increase the size of the sample.

50-38=12

step-by-step explanation:

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